The total of tetrahedral voids in the face centred unit cell is …………. .

Options

A. 6
B. 8
C. 10
D. 12

Explanation

To find the total number of tetrahedral voids in a face-centered cubic (FCC) unit cell, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the FCC Structure**:
- In a face-centered cubic (FCC) unit cell, there are atoms located at the corners and the centers of each face of the cube.

2. **Count the Atoms in the FCC Unit Cell**:
- There are 8 corner atoms, and each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell.
- There are 6 face-centered atoms, and each face atom contributes \( \frac{1}{2} \) of an atom to the unit cell.
- Therefore, the total number of atoms \( n \) in the FCC unit cell can be calculated as:
\[ n = \left(8 \times \frac{1}{8}\right) + \left(6 \times \frac{1}{2}\right) = 1 + 3 = 4 \]

3. **Use the Formula for Tetrahedral Voids**:
- The number of tetrahedral voids in a unit cell is given by the formula \( 2n \), where \( n \) is the number of atoms in the unit cell.
- Substituting the value of \( n \):
\[ \text{Number of tetrahedral voids} = 2 \times 4 = 8 \]

4. **Conclusion**:
- Therefore, the total number of tetrahedral voids in a face-centered cubic unit cell is **8**.

### Final Answer:
The total number of tetrahedral voids in the face-centered unit cell is **8**.

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